Analyzing neuroimaging data at the population level relies on averaging images that have been acquired on a group of individuals drawn from this population. Traditional group analyses are based on the general linear model, which performs euclidean averaging across individuals, independently at each brain location. It is therefore largely impacted by interindividual differences. In this paper we propose to overcome this variability by using optimal transport to leverage the geometrical properties of multivariate brain patterns. We extend the concept of Wasserstein barycenter, which was initially meant to average probability measures, to make it applicable to arbitrary data that do not necessarily fulfill the properties of a true probability measure. For this, we introduce a new algorithm that estimates a barycenter using the transportation L^p distance [8]. We provide an experimental study on how the noise level impacts the quality of the obtained barycenter on artificial data. Our proposed method is compared with the approach introduced in [6] on artificial and real functional MRI.